int ssbgv_(char *jobz, char *uplo, int *n, int *ka, int *kb, float *ab, int *ldab, float *bb, int *ldbb, float * w, float *z__, int *ldz, float *work, int *info) { /* System generated locals */ int ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1; /* Local variables */ int inde; char vect[1]; extern int lsame_(char *, char *); int iinfo; int upper, wantz; extern int xerbla_(char *, int *); int indwrk; extern int spbstf_(char *, int *, int *, float *, int *, int *), ssbtrd_(char *, char *, int *, int *, float *, int *, float *, float *, float *, int *, float *, int *), ssbgst_(char *, char *, int *, int *, int *, float *, int *, float *, int *, float *, int *, float *, int *), ssterf_(int *, float *, float *, int *), ssteqr_(char *, int *, float *, float *, float *, int *, float *, int *); /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SSBGV computes all the eigenvalues, and optionally, the eigenvectors */ /* of a float generalized symmetric-definite banded eigenproblem, of */ /* the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric */ /* and banded, and B is also positive definite. */ /* Arguments */ /* ========= */ /* JOBZ (input) CHARACTER*1 */ /* = 'N': Compute eigenvalues only; */ /* = 'V': Compute eigenvalues and eigenvectors. */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangles of A and B are stored; */ /* = 'L': Lower triangles of A and B are stored. */ /* N (input) INTEGER */ /* The order of the matrices A and B. N >= 0. */ /* KA (input) INTEGER */ /* The number of superdiagonals of the matrix A if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KA >= 0. */ /* KB (input) INTEGER */ /* The number of superdiagonals of the matrix B if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KB >= 0. */ /* AB (input/output) REAL array, dimension (LDAB, N) */ /* On entry, the upper or lower triangle of the symmetric band */ /* matrix A, stored in the first ka+1 rows of the array. The */ /* j-th column of A is stored in the j-th column of the array AB */ /* as follows: */ /* if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for MAX(1,j-ka)<=i<=j; */ /* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=MIN(n,j+ka). */ /* On exit, the contents of AB are destroyed. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= KA+1. */ /* BB (input/output) REAL array, dimension (LDBB, N) */ /* On entry, the upper or lower triangle of the symmetric band */ /* matrix B, stored in the first kb+1 rows of the array. The */ /* j-th column of B is stored in the j-th column of the array BB */ /* as follows: */ /* if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for MAX(1,j-kb)<=i<=j; */ /* if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=MIN(n,j+kb). */ /* On exit, the factor S from the split Cholesky factorization */ /* B = S**T*S, as returned by SPBSTF. */ /* LDBB (input) INTEGER */ /* The leading dimension of the array BB. LDBB >= KB+1. */ /* W (output) REAL array, dimension (N) */ /* If INFO = 0, the eigenvalues in ascending order. */ /* Z (output) REAL array, dimension (LDZ, N) */ /* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */ /* eigenvectors, with the i-th column of Z holding the */ /* eigenvector associated with W(i). The eigenvectors are */ /* normalized so that Z**T*B*Z = I. */ /* If JOBZ = 'N', then Z is not referenced. */ /* LDZ (input) INTEGER */ /* The leading dimension of the array Z. LDZ >= 1, and if */ /* JOBZ = 'V', LDZ >= N. */ /* WORK (workspace) REAL array, dimension (3*N) */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, and i is: */ /* <= N: the algorithm failed to converge: */ /* i off-diagonal elements of an intermediate */ /* tridiagonal form did not converge to zero; */ /* > N: if INFO = N + i, for 1 <= i <= N, then SPBSTF */ /* returned INFO = i: B is not positive definite. */ /* The factorization of B could not be completed and */ /* no eigenvalues or eigenvectors were computed. */ /* ===================================================================== */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; bb_dim1 = *ldbb; bb_offset = 1 + bb_dim1; bb -= bb_offset; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; /* Function Body */ wantz = lsame_(jobz, "V"); upper = lsame_(uplo, "U"); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (upper || lsame_(uplo, "L"))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ka < 0) { *info = -4; } else if (*kb < 0 || *kb > *ka) { *info = -5; } else if (*ldab < *ka + 1) { *info = -7; } else if (*ldbb < *kb + 1) { *info = -9; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -12; } if (*info != 0) { i__1 = -(*info); xerbla_("SSBGV ", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Form a split Cholesky factorization of B. */ spbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info); if (*info != 0) { *info = *n + *info; return 0; } /* Transform problem to standard eigenvalue problem. */ inde = 1; indwrk = inde + *n; ssbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb, &z__[z_offset], ldz, &work[indwrk], &iinfo) ; /* Reduce to tridiagonal form. */ if (wantz) { *(unsigned char *)vect = 'U'; } else { *(unsigned char *)vect = 'N'; } ssbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &work[inde], &z__[ z_offset], ldz, &work[indwrk], &iinfo); /* For eigenvalues only, call SSTERF. For eigenvectors, call SSTEQR. */ if (! wantz) { ssterf_(n, &w[1], &work[inde], info); } else { ssteqr_(jobz, n, &w[1], &work[inde], &z__[z_offset], ldz, &work[ indwrk], info); } return 0; /* End of SSBGV */ } /* ssbgv_ */
/* Subroutine */ int ssbgv_(char *jobz, char *uplo, integer *n, integer *ka, integer *kb, real *ab, integer *ldab, real *bb, integer *ldbb, real * w, real *z__, integer *ldz, real *work, integer *info) { /* -- LAPACK driver routine (version 3.0) -- Univ. of Tennessee, Univ. of California Berkeley, NAG Ltd., Courant Institute, Argonne National Lab, and Rice University September 30, 1994 Purpose ======= SSBGV computes all the eigenvalues, and optionally, the eigenvectors of a real generalized symmetric-definite banded eigenproblem, of the form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and banded, and B is also positive definite. Arguments ========= JOBZ (input) CHARACTER*1 = 'N': Compute eigenvalues only; = 'V': Compute eigenvalues and eigenvectors. UPLO (input) CHARACTER*1 = 'U': Upper triangles of A and B are stored; = 'L': Lower triangles of A and B are stored. N (input) INTEGER The order of the matrices A and B. N >= 0. KA (input) INTEGER The number of superdiagonals of the matrix A if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KA >= 0. KB (input) INTEGER The number of superdiagonals of the matrix B if UPLO = 'U', or the number of subdiagonals if UPLO = 'L'. KB >= 0. AB (input/output) REAL array, dimension (LDAB, N) On entry, the upper or lower triangle of the symmetric band matrix A, stored in the first ka+1 rows of the array. The j-th column of A is stored in the j-th column of the array AB as follows: if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for max(1,j-ka)<=i<=j; if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=min(n,j+ka). On exit, the contents of AB are destroyed. LDAB (input) INTEGER The leading dimension of the array AB. LDAB >= KA+1. BB (input/output) REAL array, dimension (LDBB, N) On entry, the upper or lower triangle of the symmetric band matrix B, stored in the first kb+1 rows of the array. The j-th column of B is stored in the j-th column of the array BB as follows: if UPLO = 'U', BB(kb+1+i-j,j) = B(i,j) for max(1,j-kb)<=i<=j; if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=min(n,j+kb). On exit, the factor S from the split Cholesky factorization B = S**T*S, as returned by SPBSTF. LDBB (input) INTEGER The leading dimension of the array BB. LDBB >= KB+1. W (output) REAL array, dimension (N) If INFO = 0, the eigenvalues in ascending order. Z (output) REAL array, dimension (LDZ, N) If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of eigenvectors, with the i-th column of Z holding the eigenvector associated with W(i). The eigenvectors are normalized so that Z**T*B*Z = I. If JOBZ = 'N', then Z is not referenced. LDZ (input) INTEGER The leading dimension of the array Z. LDZ >= 1, and if JOBZ = 'V', LDZ >= N. WORK (workspace) REAL array, dimension (3*N) INFO (output) INTEGER = 0: successful exit < 0: if INFO = -i, the i-th argument had an illegal value > 0: if INFO = i, and i is: <= N: the algorithm failed to converge: i off-diagonal elements of an intermediate tridiagonal form did not converge to zero; > N: if INFO = N + i, for 1 <= i <= N, then SPBSTF returned INFO = i: B is not positive definite. The factorization of B could not be completed and no eigenvalues or eigenvectors were computed. ===================================================================== Test the input parameters. Parameter adjustments */ /* System generated locals */ integer ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1; /* Local variables */ static integer inde; static char vect[1]; extern logical lsame_(char *, char *); static integer iinfo; static logical upper, wantz; extern /* Subroutine */ int xerbla_(char *, integer *); static integer indwrk; extern /* Subroutine */ int spbstf_(char *, integer *, integer *, real *, integer *, integer *), ssbtrd_(char *, char *, integer *, integer *, real *, integer *, real *, real *, real *, integer *, real *, integer *), ssbgst_(char *, char *, integer *, integer *, integer *, real *, integer *, real *, integer *, real *, integer *, real *, integer *), ssterf_(integer *, real *, real *, integer *), ssteqr_(char *, integer *, real *, real *, real *, integer *, real *, integer *); ab_dim1 = *ldab; ab_offset = 1 + ab_dim1 * 1; ab -= ab_offset; bb_dim1 = *ldbb; bb_offset = 1 + bb_dim1 * 1; bb -= bb_offset; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1 * 1; z__ -= z_offset; --work; /* Function Body */ wantz = lsame_(jobz, "V"); upper = lsame_(uplo, "U"); *info = 0; if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (upper || lsame_(uplo, "L"))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ka < 0) { *info = -4; } else if (*kb < 0 || *kb > *ka) { *info = -5; } else if (*ldab < *ka + 1) { *info = -7; } else if (*ldbb < *kb + 1) { *info = -9; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -12; } if (*info != 0) { i__1 = -(*info); xerbla_("SSBGV ", &i__1); return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Form a split Cholesky factorization of B. */ spbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info); if (*info != 0) { *info = *n + *info; return 0; } /* Transform problem to standard eigenvalue problem. */ inde = 1; indwrk = inde + *n; ssbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb, &z__[z_offset], ldz, &work[indwrk], &iinfo) ; /* Reduce to tridiagonal form. */ if (wantz) { *(unsigned char *)vect = 'U'; } else { *(unsigned char *)vect = 'N'; } ssbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &work[inde], &z__[ z_offset], ldz, &work[indwrk], &iinfo); /* For eigenvalues only, call SSTERF. For eigenvectors, call SSTEQR. */ if (! wantz) { ssterf_(n, &w[1], &work[inde], info); } else { ssteqr_(jobz, n, &w[1], &work[inde], &z__[z_offset], ldz, &work[ indwrk], info); } return 0; /* End of SSBGV */ } /* ssbgv_ */
int ssbgvd_(char *jobz, char *uplo, int *n, int *ka, int *kb, float *ab, int *ldab, float *bb, int *ldbb, float * w, float *z__, int *ldz, float *work, int *lwork, int * iwork, int *liwork, int *info) { /* System generated locals */ int ab_dim1, ab_offset, bb_dim1, bb_offset, z_dim1, z_offset, i__1; /* Local variables */ int inde; char vect[1]; extern int lsame_(char *, char *); int iinfo; extern int sgemm_(char *, char *, int *, int *, int *, float *, float *, int *, float *, int *, float *, float *, int *); int lwmin; int upper, wantz; int indwk2, llwrk2; extern int xerbla_(char *, int *), sstedc_( char *, int *, float *, float *, float *, int *, float *, int *, int *, int *, int *), slacpy_(char *, int *, int *, float *, int *, float *, int *); int indwrk, liwmin; extern int spbstf_(char *, int *, int *, float *, int *, int *), ssbtrd_(char *, char *, int *, int *, float *, int *, float *, float *, float *, int *, float *, int *), ssbgst_(char *, char *, int *, int *, int *, float *, int *, float *, int *, float *, int *, float *, int *), ssterf_(int *, float *, float *, int *); int lquery; /* -- LAPACK driver routine (version 3.2) -- */ /* Univ. of Tennessee, Univ. of California Berkeley and NAG Ltd.. */ /* November 2006 */ /* .. Scalar Arguments .. */ /* .. */ /* .. Array Arguments .. */ /* .. */ /* Purpose */ /* ======= */ /* SSBGVD computes all the eigenvalues, and optionally, the eigenvectors */ /* of a float generalized symmetric-definite banded eigenproblem, of the */ /* form A*x=(lambda)*B*x. Here A and B are assumed to be symmetric and */ /* banded, and B is also positive definite. If eigenvectors are */ /* desired, it uses a divide and conquer algorithm. */ /* The divide and conquer algorithm makes very mild assumptions about */ /* floating point arithmetic. It will work on machines with a guard */ /* digit in add/subtract, or on those binary machines without guard */ /* digits which subtract like the Cray X-MP, Cray Y-MP, Cray C-90, or */ /* Cray-2. It could conceivably fail on hexadecimal or decimal machines */ /* without guard digits, but we know of none. */ /* Arguments */ /* ========= */ /* JOBZ (input) CHARACTER*1 */ /* = 'N': Compute eigenvalues only; */ /* = 'V': Compute eigenvalues and eigenvectors. */ /* UPLO (input) CHARACTER*1 */ /* = 'U': Upper triangles of A and B are stored; */ /* = 'L': Lower triangles of A and B are stored. */ /* N (input) INTEGER */ /* The order of the matrices A and B. N >= 0. */ /* KA (input) INTEGER */ /* The number of superdiagonals of the matrix A if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KA >= 0. */ /* KB (input) INTEGER */ /* The number of superdiagonals of the matrix B if UPLO = 'U', */ /* or the number of subdiagonals if UPLO = 'L'. KB >= 0. */ /* AB (input/output) REAL array, dimension (LDAB, N) */ /* On entry, the upper or lower triangle of the symmetric band */ /* matrix A, stored in the first ka+1 rows of the array. The */ /* j-th column of A is stored in the j-th column of the array AB */ /* as follows: */ /* if UPLO = 'U', AB(ka+1+i-j,j) = A(i,j) for MAX(1,j-ka)<=i<=j; */ /* if UPLO = 'L', AB(1+i-j,j) = A(i,j) for j<=i<=MIN(n,j+ka). */ /* On exit, the contents of AB are destroyed. */ /* LDAB (input) INTEGER */ /* The leading dimension of the array AB. LDAB >= KA+1. */ /* BB (input/output) REAL array, dimension (LDBB, N) */ /* On entry, the upper or lower triangle of the symmetric band */ /* matrix B, stored in the first kb+1 rows of the array. The */ /* j-th column of B is stored in the j-th column of the array BB */ /* as follows: */ /* if UPLO = 'U', BB(ka+1+i-j,j) = B(i,j) for MAX(1,j-kb)<=i<=j; */ /* if UPLO = 'L', BB(1+i-j,j) = B(i,j) for j<=i<=MIN(n,j+kb). */ /* On exit, the factor S from the split Cholesky factorization */ /* B = S**T*S, as returned by SPBSTF. */ /* LDBB (input) INTEGER */ /* The leading dimension of the array BB. LDBB >= KB+1. */ /* W (output) REAL array, dimension (N) */ /* If INFO = 0, the eigenvalues in ascending order. */ /* Z (output) REAL array, dimension (LDZ, N) */ /* If JOBZ = 'V', then if INFO = 0, Z contains the matrix Z of */ /* eigenvectors, with the i-th column of Z holding the */ /* eigenvector associated with W(i). The eigenvectors are */ /* normalized so Z**T*B*Z = I. */ /* If JOBZ = 'N', then Z is not referenced. */ /* LDZ (input) INTEGER */ /* The leading dimension of the array Z. LDZ >= 1, and if */ /* JOBZ = 'V', LDZ >= MAX(1,N). */ /* WORK (workspace/output) REAL array, dimension (MAX(1,LWORK)) */ /* On exit, if INFO = 0, WORK(1) returns the optimal LWORK. */ /* LWORK (input) INTEGER */ /* The dimension of the array WORK. */ /* If N <= 1, LWORK >= 1. */ /* If JOBZ = 'N' and N > 1, LWORK >= 3*N. */ /* If JOBZ = 'V' and N > 1, LWORK >= 1 + 5*N + 2*N**2. */ /* If LWORK = -1, then a workspace query is assumed; the routine */ /* only calculates the optimal sizes of the WORK and IWORK */ /* arrays, returns these values as the first entries of the WORK */ /* and IWORK arrays, and no error message related to LWORK or */ /* LIWORK is issued by XERBLA. */ /* IWORK (workspace/output) INTEGER array, dimension (MAX(1,LIWORK)) */ /* On exit, if LIWORK > 0, IWORK(1) returns the optimal LIWORK. */ /* LIWORK (input) INTEGER */ /* The dimension of the array IWORK. */ /* If JOBZ = 'N' or N <= 1, LIWORK >= 1. */ /* If JOBZ = 'V' and N > 1, LIWORK >= 3 + 5*N. */ /* If LIWORK = -1, then a workspace query is assumed; the */ /* routine only calculates the optimal sizes of the WORK and */ /* IWORK arrays, returns these values as the first entries of */ /* the WORK and IWORK arrays, and no error message related to */ /* LWORK or LIWORK is issued by XERBLA. */ /* INFO (output) INTEGER */ /* = 0: successful exit */ /* < 0: if INFO = -i, the i-th argument had an illegal value */ /* > 0: if INFO = i, and i is: */ /* <= N: the algorithm failed to converge: */ /* i off-diagonal elements of an intermediate */ /* tridiagonal form did not converge to zero; */ /* > N: if INFO = N + i, for 1 <= i <= N, then SPBSTF */ /* returned INFO = i: B is not positive definite. */ /* The factorization of B could not be completed and */ /* no eigenvalues or eigenvectors were computed. */ /* Further Details */ /* =============== */ /* Based on contributions by */ /* Mark Fahey, Department of Mathematics, Univ. of Kentucky, USA */ /* ===================================================================== */ /* .. Parameters .. */ /* .. */ /* .. Local Scalars .. */ /* .. */ /* .. External Functions .. */ /* .. */ /* .. External Subroutines .. */ /* .. */ /* .. Executable Statements .. */ /* Test the input parameters. */ /* Parameter adjustments */ ab_dim1 = *ldab; ab_offset = 1 + ab_dim1; ab -= ab_offset; bb_dim1 = *ldbb; bb_offset = 1 + bb_dim1; bb -= bb_offset; --w; z_dim1 = *ldz; z_offset = 1 + z_dim1; z__ -= z_offset; --work; --iwork; /* Function Body */ wantz = lsame_(jobz, "V"); upper = lsame_(uplo, "U"); lquery = *lwork == -1 || *liwork == -1; *info = 0; if (*n <= 1) { liwmin = 1; lwmin = 1; } else if (wantz) { liwmin = *n * 5 + 3; /* Computing 2nd power */ i__1 = *n; lwmin = *n * 5 + 1 + (i__1 * i__1 << 1); } else { liwmin = 1; lwmin = *n << 1; } if (! (wantz || lsame_(jobz, "N"))) { *info = -1; } else if (! (upper || lsame_(uplo, "L"))) { *info = -2; } else if (*n < 0) { *info = -3; } else if (*ka < 0) { *info = -4; } else if (*kb < 0 || *kb > *ka) { *info = -5; } else if (*ldab < *ka + 1) { *info = -7; } else if (*ldbb < *kb + 1) { *info = -9; } else if (*ldz < 1 || wantz && *ldz < *n) { *info = -12; } if (*info == 0) { work[1] = (float) lwmin; iwork[1] = liwmin; if (*lwork < lwmin && ! lquery) { *info = -14; } else if (*liwork < liwmin && ! lquery) { *info = -16; } } if (*info != 0) { i__1 = -(*info); xerbla_("SSBGVD", &i__1); return 0; } else if (lquery) { return 0; } /* Quick return if possible */ if (*n == 0) { return 0; } /* Form a split Cholesky factorization of B. */ spbstf_(uplo, n, kb, &bb[bb_offset], ldbb, info); if (*info != 0) { *info = *n + *info; return 0; } /* Transform problem to standard eigenvalue problem. */ inde = 1; indwrk = inde + *n; indwk2 = indwrk + *n * *n; llwrk2 = *lwork - indwk2 + 1; ssbgst_(jobz, uplo, n, ka, kb, &ab[ab_offset], ldab, &bb[bb_offset], ldbb, &z__[z_offset], ldz, &work[indwrk], &iinfo) ; /* Reduce to tridiagonal form. */ if (wantz) { *(unsigned char *)vect = 'U'; } else { *(unsigned char *)vect = 'N'; } ssbtrd_(vect, uplo, n, ka, &ab[ab_offset], ldab, &w[1], &work[inde], &z__[ z_offset], ldz, &work[indwrk], &iinfo); /* For eigenvalues only, call SSTERF. For eigenvectors, call SSTEDC. */ if (! wantz) { ssterf_(n, &w[1], &work[inde], info); } else { sstedc_("I", n, &w[1], &work[inde], &work[indwrk], n, &work[indwk2], & llwrk2, &iwork[1], liwork, info); sgemm_("N", "N", n, n, n, &c_b12, &z__[z_offset], ldz, &work[indwrk], n, &c_b13, &work[indwk2], n); slacpy_("A", n, n, &work[indwk2], n, &z__[z_offset], ldz); } work[1] = (float) lwmin; iwork[1] = liwmin; return 0; /* End of SSBGVD */ } /* ssbgvd_ */